A physical model has been developed to describe the mechanics of growing blood vessels. The blood vessel is treated as a growing elastic shell imbedded in a surrounding viscous fluid (the tissue). As the vessel grows, it buckles in any of three possible modes, varicose, sinuous, or helical, and with a particular wavelength in each case. Solutions of the governing equations for the geometry and mechanical force balance are currently being sought for the sinuous and helical modes. This work is an extension of previous work on the axisymmetric, varicose mode.